Yes and it would mean "one of my cats". Let's say you have 5 cats and you want to refer to something that one of your cats did withiut caring which of them did it: one of my cats broke the vase=Μία/μια απο τις γάτες μου or μια/μία γάτα μου έσπασε το βάζο.

Yes, you can say ο γάτος. There is also το γατί, which is used either instead of the feminine word (which refers to any cat really) or specifically for young cats. You can see more about gendered nouns for animals here https://forum.duolingo.com/comment/27198534.